Magnetic resonance imaging (MRI) apparatuses are medical-purpose image diagnosis systems that cause hydrogen atomic nuclei, which are contained in any transverse plane of a subject, to exhibit nuclear magnetic resonance, and produce a tomographic image of the plane using an induced nuclear magnetic resonance signal.
In general, when a slicing magnetic field gradient to be used to select a subject's plane whose tomographic image is to be produced is applied, an excitation pulse that excites magnetization in the plane is applied at the same time. Thus, a nuclear magnetic resonance signal (echo) is induced in the stage of convergence of the excited magnetization. In efforts to append positional information to magnetization, a phase-encoding magnetic field gradient and a readout magnetic field gradient that are perpendicular to each other in a section are applied until an echo results from excitation is acquired. A measured echo is mapped to a k-space having an axis of abscissas kx and an axis of ordinates ky. Image reconstruction is then performed through inverse Fourier transform.
A pulse with which an echo is induced and each magnetic field gradient are applied based on a predefined pulse sequence. As for the pulse sequence, various pulse sequences intended for respective purposes are known. For example, a gradient echo (GE)-type fast imaging method is a method in which a pulse sequence is repeatedly applied, a phase-encoding magnetic field gradient is sequentially changed for every repetition in order to measure the number of echoes required for producing one tomographic image.
FIG. 1(A) shows a pulse sequence to be employed in GE radial scanning (refer to, for example, “Magnetic Resonance Imaging—Physical Principles and Sequence Design” by E. Mark Haacke, et al. (Wiley-Liss, pp. 303-330, 1999)). Actions to be performed for the pulse sequence will be described below.
Along with application of a z-direction slicing magnetic field gradient 201, a radiofrequency (RF) magnetic field pulse 202 for excitation of magnetization of protons at a resonant frequency f0 is applied in order to induce a nuclear magnetic resonance phenomenon in protons in a certain slice of an object entity. After dephasing magnetic field gradient pulses 203, 204, and 205 are applied, while readout magnetic field gradient pulses 206 and 207 are applied, a nuclear magnetic resonance signal (echo) 208 is measured. After the measurement of an echo is completed, re-phasing magnetic field gradient pulses 209, 210, and 211 are applied in order to restore the phase of magnetization in preparation for the next excitation.
The above procedure is repeated Ne times with a repetition time TR determined, whereby Ne echoes are measured. The dephasing magnetic field gradient pulses 204 and 205, readout magnetic field gradient pulses 206 and 207, re-phasing magnetic field gradient pulses 209 and 210 have the amplitudes thereof changed for every repetition as shown in FIG. 1A. In the case of the illustrated sequence, the dephasing magnetic field gradient pulse 204 and re-phasing magnetic field gradient pulse 209 change step by step from −Ne/2 to Ne/2−1. The dephasing magnetic field gradient pulse 205 and re-phasing magnetic field gradient pulse 210 change step by step from 0 through −Ne/2 to −1. The readout magnetic field gradient pulse 206 changes step by step from Ne/2 to −Ne/2−1. The readout magnetic field gradient pulse 207 changes step by step from 0 through Ne/2 to 1.
Measured echoes are, as shown in FIG. 1(B), mapped to a k-space. The drawing is concerned with a case where Ne denotes 128. In the k-space, one echo is expressed with one line passing through an origin O, and echoes are disposed equidistantly in a rotating direction. A difference Δθ between the angles of adjoining echoes is π/Ne radian.
The k-space is transformed into a Cartesian grid by performing gridding (refer to, for example, “Selection of a Convolution Function for Fourier Inversion Using Gridding” by Jackson J I, Meyer G H, Nishimura D G (IEEE Trans. Med. Imaging, Vol. 10, No. 3, pp. 473-478, 1991)). Thereafter, image reconstruction is performed through two-dimensional inverse Fourier transform. An imaging time required for one image corresponds to a product of a TR by the number of echoes. For example, assuming that one image is reconstructed using one hundred and twenty-eight echoes with the TR set to 4 ms, the imaging time comes to 512 ms.
In order to reconstruct an image having N pixels in rows and columns, the number of samples per echo and the number of echoes are normally set to N. If the number of echoes is smaller than N, the imaging time is shortened and a temporal resolution improves. For example, assuming that only odd-numbered echoes shown in FIG. 1(B) are measured, the number of echoes is 64 and the imaging time is a half of the above imaging time.